1 / (5x+1) - 2 / (5x -1) - 9x / (25x² - 1) = 5 x² / (1 -25x² ) ;
* * * 5 x² / (1 -25x² ) = - 5 x² / (25x² -1) * * *
1 / (5x+1) - 2 / (5x -1) +5 x² / (25x² - 1 ) - 9x / (25x² - 1) ;
* * * 25x² - 1 =(5x)² -1 =(5x -1)(5x+1) * * *
( 5x -1 -2(5x+1) +5x² -9x ) / (5x +1)(5x-1) =0 ;
* * * ОДЗ : x ≠ ± 1/5 * * *
( 5x -1 -10x -2 +5x² -9x ) / (5x +1)(5x+1) = 0 ;
(5x² -14x -3) / 25 ( x - 1/5)(x+1/5) =0 ;
5(x + 1/5) (x -3) / 25 ( x - 1/5)(x+1/5) =0 ; * * * x ≠ -1/5 * * *
x - 3 =0 ⇒ x = 3 .
ответ : x = 3 .
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P.S. 5x² -14x -3 =0 ; * * * D/4 = √(7² -5(-3)) = √(49+15) = √64 = 8 * * *
x₁ =( 7 -8)/5 = -1/5 ; x₂ = ( 7 +8)/5 = 15 /5 =3 ; .
5x² -14x -3 =5(x -x₁)(x₂ -3) = 5(x +1/5)(x -3)